So on the one hand:
Cleopatra was 100% Greek by descent. Further she was literally the only member of her dynasty to learn how to speak Egyptian. Every other single one of her predecessors never bothered, they spoke Koine Greek, which was also Cleopatra’s first language. The Ptolemies did NOT marry non-Greeks like Persians or Egyptians - they married other Greeks who happened to be ruling in places like Persia. This was the Hellenistic age. Every ruling dynasty between Albania and the Indus was ethnically and linguistically Greek. Ethnicity-wise they were as Greek as Greek can be. Also fairly inbred by Cleopatra’s time.
In certain respects the Ptolemies also functioned as an extractive alien class. The capital was largely Greek and existed as an island in a native Egyptian sea. The military, other than a brief experiment under Ptolemy IV, consisted overwhelmingly of Greek mercenaries with zero native troops. As noted the ruling class with that one very late exception did not bother learning the language of their subjects. They were like a much more stubborn version of the early Norman French in England in that respect.
On the other hand:
The Ptolemies extensively adopted pharaonic pageantry and religious imagery. The sibling marriage thing with its associated dynastic cult was thoroughly Egyptian in conception - Macedonians thought that kind of stuff was gross. The ‘living God’ thing likewise, very un-Macedonian. They patronized and funded the native priesthood and temples as a means of social control with a fair degree of success. Egyptian art was patronized alongside Greek and as time went on you started seeing elements of both in common design.
If Cleopatra VII (the famous one) went pretty Egyptian in imagery (not entirely though - Greek elements were still retained), she was just following a well-worn template of religious and artistic syncretism established by her forbears.
So if people say Cleopatra was Greek, I’d say I more or less agree. If they say she’s Egyptian, I’d say sorta, but not entirely. The late Ptolemies were pretty syncretic, but they were also very, very aware and proud of their distinctive origins as Greek-speaking conquerors. I’d call her more Hellenistic than anything, which to me implies a Greek-inflected and politically dominated cosmopolitan culture.